Highest Common Factor of 705, 8138 using Euclid's algorithm
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 705, 8138 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 705, 8138 is 1 the largest number which exactly divides all the numbers i.e. where the remainder is zero. Let us get into the working of this example.
Consider we have numbers 705, 8138 and we need to find the HCF of these numbers. To do so, we need to choose the largest integer first and then as per Euclid's Division Lemma a = bq + r where 0 ≤ r ≤ b
Highest common factor (HCF) of 705, 8138 is 1.
HCF(705, 8138) = 1
HCF of 705, 8138 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 705, 8138 is 1.
Highest Common Factor of 705,8138 is 1
Step 1: Since 8138 > 705, we apply the division lemma to 8138 and 705, to get
8138 = 705 x 11 + 383
Step 2: Since the reminder 705 ≠ 0, we apply division lemma to 383 and 705, to get
705 = 383 x 1 + 322
Step 3: We consider the new divisor 383 and the new remainder 322, and apply the division lemma to get
383 = 322 x 1 + 61
We consider the new divisor 322 and the new remainder 61,and apply the division lemma to get
322 = 61 x 5 + 17
We consider the new divisor 61 and the new remainder 17,and apply the division lemma to get
61 = 17 x 3 + 10
We consider the new divisor 17 and the new remainder 10,and apply the division lemma to get
17 = 10 x 1 + 7
We consider the new divisor 10 and the new remainder 7,and apply the division lemma to get
10 = 7 x 1 + 3
We consider the new divisor 7 and the new remainder 3,and apply the division lemma to get
7 = 3 x 2 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 705 and 8138 is 1
Notice that 1 = HCF(3,1) = HCF(7,3) = HCF(10,7) = HCF(17,10) = HCF(61,17) = HCF(322,61) = HCF(383,322) = HCF(705,383) = HCF(8138,705) .
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Frequently Asked Questions on HCF of 705, 8138 using Euclid's Algorithm
1. What is the Euclid division algorithm?
Answer: Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of given positive integers.
2. what is the HCF of 705, 8138?
Answer: HCF of 705, 8138 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 705, 8138 using Euclid's Algorithm?
Answer: For arbitrary numbers 705, 8138 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.